My opinion would be "on" for both. If you wanted to use "onto", I think you could only do so in the first preposition because it's a place, rather then a personal feel, if you understand. I don't hear "onto" alot anymore, perhaps because "on" is so much easier. But I find it more proper to use "onto" when speaking of a place, and of literal text. For example:
I think that you would use onto in the first case, as in: "When we stepped onto the sandy beach, a gentle breeze blew on our faces."
Beach is similar to platform.
My understanding is that you use "stepped on" if you stepped on something by accident.
For example: "Ouch! You stepped on my foot!"
When you are stepping onto something on purpose (like a beach, platform, scale) you would use onto as your preposition.